We propose to design and test mathematically well founded algorithmic and statistical tectonics for analyzing large scale, heterogeneous and noisy data. We focus on fully analytical evaluation of algorithms' performance and rigorous statistical guarantees on the analysis results. This project will leverage on the PIs' recent work on cancer genomics data analysis and rigorous data mining techniques. Those works were driven by specific applications, while in the current project we aim at developing general principles and techniques that will apply to a broad sets of applications. The proposed research is transformative in its emphasis on rigorous analytical evaluation of algorithms' performance and statistical measures of output uncertainty, in contrast to the primarily heuristic approaches currently used in data ming and machine learning. While we cannot expect full mathematical analysis of all data mining and machine learning techniques, any progress in that direction will have significant contribution to the reliability and scientific impact of this discipline. While ou work is motivated by molecular biology data, we expect the techniques to be useful for other scientific communities with massive multi-variate data analysis challenges. Molecular biology provides an excellent source of data for testing advance data analysis techniques: specifically, DNA/RNA sequence data repositories are growing at a super-exponential rate. The data is typically large and noisy, and it includes both genotype and phenotype features that permit experimental validation of the analysis. One such data repository is The Cancer Genome Atlas (TCGA), which we will use for initial testing of the proposed approaches. RELEVANCE (See instructions): This project will advocate a responsible approach to data analysis, based on well-founded mathematical and Statistical concepts. Such an approach enhances the effectiveness of evidence based medicine and other policy and social applications of big data analysis. The proposed work will be tested on human and cancer genome data, contributing to health IT, one of the National Priority Domain Areas.